Finite Group DatabasebetaFinite Group Databasebeta| order | 18752 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | D8×C293 ⋊ C4 |
| Sylow | C293 ⋊ #442 |
132 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2344 |
Polycyclic presentation:
2^6,293|a^2=e,c^2=ef,d^2=f,b^a=bd,c^a=cf,d^a=df,g^a=g^155,d^b=df,g^c=g^138,g^e=g^292533 conjugacy classes — view the full character table.
| maximal subgroup of | #49175194, #49175195, #49175196, … |
| maximal normal subgroup of | #49175194, #49175195, #49175196, … |
| maximal quotient of | #49174381, #49174382, #49174383, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18752, 1590);